This research plan will focus on two areas of biostatistics: Statistical Computing - In the analysis of biomedical data it is standard practice to perform tests of significance and then summarize statistically significant effects in terms of p-values. One can perform either exact or asympotoic tests of significance. The main advantage of exact tests, the absolute reliability of the p-values they generate, is frequently offset by the computational complexity involved in their execution. If the sample size of an experiment is steadily increased, a point is reached beyond which exact tests of significance become computationally infeasible. Yet the sample size may not be large enough for corresponding asymptotic tests of significance to be reliable. This research project will provide new and unified computational techniques for performing exact tests of significance which narrow or, in some cases, close the sample size gap between the computational feasibility of exact tests and the asymptotic reliability of approximate tests. Sequential Analysis - In sequential experiments for comparing two or more populations with respect to some important characteristic, the data being generated are continuously monitored and further experimentation is terminated as soon as one can draw a reasonable conclusion about population differences. Because of their early termination properties, sequential experiments have ethical and economic advantages over the more traditional fixed sample experiments. At the same time they preserve the sensitivity and accuracy of the scientific inferences for which they were designed. This project will provide optimal sequential designs for clinical trials based on both the frequentist and decision theoretic formulations. The frequentist formulation emphasizes the accuracy of the resulting scientific inferences whereas decision theory emphasizes optimal patient care. The relationship between the two formulations will be investigated. These 2 proposed methodological advances are directly relevant to the planning and analysis of cancer clinical trials and retrospective studies.